This is my preferred method as well. However, I was never able to get a braid to work very well. My favored choice is a vacuum de-soldering tool (though more expensive than braid), sucks the hot solder right off the board leaving the leads extremely clean, then you can do as MacJunky says to loosen the residual solder.
FYI, if they are bad caps, RAM, ICs, resistors, etc., you can just clip the leads at the base with needle-nosed wire-cutters and then simply pull the pins one at a time. No need to delicately de-solder or risk exploding caps! ... unless you physically can't get under them to cut the leads, or are trying to salvage something. So much faster to yank those bad components. It takes much less heat and time to solder the new leads to the board.